intersect misses common elements of 2 matrices

I've been using intersect to identify the common elements of two 2D grids. However, when I try it against the following code, it misses some of the common elements.

[x1Grid_1,x2Grid_1] = meshgrid(-70:0.5:70, 1:0.05:17);
xGrid_1 = [x1Grid_1(:), x2Grid_1(:)];
[x1Grid_2,x2Grid_2] = meshgrid(-56:0.5:35, 6:0.05:16);
xGrid_2 = [x1Grid_2(:), x2Grid_2(:)];
[c1,c2,c3] = intersect(xGrid_1,xGrid_2,'rows');

The vector xGrid_2 should be made entirely of elements from xGrid_1. xGrid_2 has 36783 rows, but after running intersect, vectors c1-c3 only have 30195 elements, meaning they miss some of the common elements. I can't understand why this would be happening. Any input would be helpful.

I'm using 2016a.

Thanks, Jack

[John BG]

what are you after, the line intersection of 2 planes?

Answer 1

[Image Analyst]

I think this might be a case of floating point numbers, arrived at via different operations, not matching when you think they should. You need to check within a tolerance. See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[John D'Errico]

Note that multiples of 0.5 are exactly representable in floating point arithmetic.

HOWEVER, multiples of 0.05 are NOT exactly representable. The difference is important.

sprintf('%0.55f',0.05)
ans =
0.0500000000000000027755575615628913510590791702270507812

[Image Analyst]

True, as are all negative powers of 2: 2^(-1) and 2^(-2), etc. (0.5, 0.25, 0.125, etc.).

[James Tursa]

Or if you are on a Windows system where the underlying sprintf algorithm is different, you can use num2strexact instead:

>> num2strexact(0.05)
ans =
5.000000000000000277555756156289135105907917022705078125e-2

Answer 2

[Jack]

Rounding it did the trick - I just used

xGrid_1 = round(xGrid_1*100)/100;
xGrid_2 = round(xGrid_2*100)/100;

to cutoff the decimals after 0.01. That made it work.

Thanks